Local indicators of spatio-temporal association: LISTA functions

We consider here the problem of detecting local clusters in spatio-temporal point patterns. These tools are based on local second-order characteristics of spatio-temporal point processes. We extend the notion of spatial dependence to spatio-temporal structures defining the LISTA functions derived from second-order spatio-temporal product densities. We derive some theoretical properties, propose unbiased edge-corrected estimators and use these new functions to analyse and detect cluster- ing in the spatio-temporal evolution of a disease.